This invention relates to interferometry systems, e.g., interferometry systems that measure angular and linear displacements of a measurement object such as a mask stage or a wafer stage in a lithography scanner or stepper system, and also interferometry systems that monitor wavelength and determine intrinsic properties of gases.
Displacement measuring interferometers monitor changes in the position of a measurement object relative to a reference object based on an optical interference signal. The interferometer generates the optical interference signal by overlapping a measurement beam reflected from the measurement object with a reference beam reflected from the reference object.
In many applications, the measurement and reference beams have orthogonal polarizations and different frequencies. The different frequencies can be produced, for example, by laser Zeeman splitting, by acousto-optical modulation, or internal to the laser using birefringent elements or the like. The orthogonal polarizations allow a polarizing beam-splitter to direct the measurement and reference beams to the measurement and reference objects, respectively, and combine the reflected measurement and reference beams to form overlapping exit measurement and reference beams. The overlapping exit beams form an output beam that subsequently passes through a polarizer. The polarizer mixes polarizations of the exit measurement and reference beams to form a mixed beam. Components of the exit measurement and reference beams in the mixed beam interfere with one another so that the intensity of the mixed beam varies with the relative phase of the exit measurement and reference beams. A detector measures the time-dependent intensity of the mixed beam and generates an electrical interference signal proportional to that intensity. Because the measurement and reference beams have different frequencies, the electrical interference signal includes a “heterodyne” signal having a beat frequency equal to the difference between the frequencies of the exit measurement and reference beams. If the lengths of the measurement and reference paths are changing relative to one another, e.g., by translating a stage that includes the measurement object, the measured beat frequency includes a Doppler shift equal to 2vnp /λ, where v is the relative speed of the measurement and reference objects, λ is the wavelength of the measurement and reference beams, n is the refractive index of the medium through which the light beams travel, e.g., air or vacuum, and p is the number of passes to the reference and measurement objects. Changes in the relative position of the measurement object correspond to changes in the phase of the measured interference signal, with a 2π phase change corresponding to a distance change L of λ/(np) , where L is a round-trip distance change, e.g., the change in distance to and from a stage that includes the measurement object.
In dispersion measuring applications, optical path length measurements are made at multiple wavelengths, e.g., 532 nm and 1064 nm, and are used to measure dispersion of a gas in the measurement path of the distance measuring interferometer. The dispersion measurement can be used to convert the optical path length measured by a distance measuring interferometer into a physical length. Such a conversion can be important since changes in the measured optical path length can be caused by gas turbulence and/or by a change in the average density of the gas in the measurement arm even though the physical distance to the measurement object is unchanged. In addition to the extrinsic dispersion measurement, the conversion of the optical path length to a physical length requires knowledge of an intrinsic value of the gas. The factor Γ is a suitable intrinsic value and is the reciprocal dispersive power of the gas for the wavelengths used in the dispersion interferometry. The factor Γ can be measured separately or based on literature values.
Unfortunately, imperfections in the interferometry system may degrade the accuracy of such interferometric measurements. For example, many interferometers include non-linearities such as what are known as “cyclic errors.” The cyclic errors can be expressed as contributions to the phase and/or the intensity of the measured interference signal and have a sinusoidal dependence on phase changes associated with changes in optical path length pnL and/or on phase changes associated with other parameters. In particular, there is first harmonic cyclic error in phase that has a sinusoidal dependence on (2πpnL)/λ and there is second harmonic cyclic error in phase that has a sinusoidal dependence on 2 (2πpnL)/λ. Higher harmonic cyclic errors may also be present.
There are also “non-cyclic non-linearities” such as those caused by a change in lateral displacement (i.e., “beam shear”) between the reference and measurement beam components of an output beam of an interferometer when the wavefronts of the reference and measurement beam components have wavefront errors. This can be explained as follows.
Inhomogeneities in the interferometer optics may cause wavefront errors in the reference and measurement beams. When the reference and measurement beams propagate collinearly with one another through such inhomogeneities, the resulting wavefront errors are identical and their contributions to the interferometric signal cancel each other out. More typically, however, the reference and measurement beam components of the output beam are laterally displaced from one another, i.e., they have a relative beam shear. Such beam shear causes the wavefront errors to contribute an error to the interferometric signal derived from the output beam. Moreover, in many interferometry systems beam shear changes as the position or angular orientation of the measurement object changes. For example, a change in relative beam shear can be introduced by a lateral displacement of a retroreflector measurement object or by a change in the angular orientation of a plane mirror measurement object. Accordingly, a change in the position or angular orientation of the measurement object produces a corresponding error in the interferometric signal.
The effect of the beam shear and wavefront errors will depend upon procedures used to mix components of the output beam with respect to component polarization states and to detect the mixed output beam to generate an electrical interference signal. The mixed output beam may for example be detected by a detector without any focusing of the mixed beam onto the detector, by detecting the mixed output beam as a beam focused onto a detector, or by launching the mixed output beam into a single mode or multi-mode optical fiber and detecting a portion of the mixed output beam that is transmitted by the optical fiber. The effect of the beam shear and wavefront errors will also depend on properties of a beam stop should a beam stop be used in the procedure to detect the mixed output beam. Generally, the errors in the interferometric signal are compounded when an optical fiber is used to transmit the mixed output beam to the detector.
In some cases, the change in position or orientation of a measurement object is calculated from measurements of the phase that are made while the lengths or orientations of the measurement and reference beam paths are changing relative to one another, e.g. by translating a stage that includes the measurement object. The relative changes in measurement and reference beam paths may occur as a result of changes in the relative positions and orientations of the measurement and reference objects, or may be due to changes in the disposition of other optical components in the interferometer. For example, optical components in the interferometer may be subject to pitch, yaw and/or roll.
Highly precise metrology demands compensation for changes in the relative directions of the measurement and reference beams, in which information is encoded about distances and/or angles. Without compensation, an interferometer may not provide measurements of suitable precision for applications such as fabrication of semiconductor devices. Angle interferometers are used to determine the relative angular disposition of two beams, such as a measurement beam and a reference beam, and to determine the angle between the beams or provide other information related to the orientation and propagation directions of the beams. Angle interferometers are also used to provide information about changes in beam propagation directions and angles as a function of time.
Interferometers may also include dynamic elements that may be used to control the directions of the measurement and reference beams. These dynamic elements may require feedback signals for their control, and these feedback signals may be provided by measurements of changes in beam direction. For example, in a passive, zero-shear single beam plane mirror interferometer, multiple degrees of freedom of a plane mirror measurement object may be measured using a single measurement beam, and determining changes in the multiple degrees of freedom may include determining changes in the propagation direction of the measurement beam.